What does deep learning offer with respect to standard machine learning?
Deep learning allows you to solve complex problems without necessarily being able to specify the important "features" or key input variables for the model in advance.

To give an example, a problem that may be easily tackled without deep learning could be predicting the frequency and claim amounts of insurance vehicle claims,  given historical claim data that may include various attributes of the policy holder and their vehicle.  In this example, the "features" to be specified in the model are the known attributes of policy holder and vehicle.  The model will then attempt to utilise these features to make predictions.

On the other hand,  facial recognition is a problem more suited to deep learning algorithms.  This is because it is difficult to manually identify what combinations of pixels may be important features to include in a conventional machine learning model.  A multi-layered neural network however has the potential to identify/create the important features itself, which may include for example eyes, nose and mouth, and then utilise these features to recognise faces and other objects.